Nuclear fission viewed as a diffusion process: Case of very large friction

Abstract

Using a Fokker-Planck equation, we consider induced nuclear fission for large values of the friction constant. Then, the equation simplifies to the Smoluchowski equation which we solve using a method of van Kampen. We find that the fission rate obeys a scaling law. From our numerical results and those obtained previously, we estimate the transient time~for fission. For small nuclear temperature,~is defined as the time delay between the onset of a nuclear reaction and the attainment of the quasistationary probability flow over the fission barrier. For nuclear temperatures large compared to the fission barrier, the entire fission process is governed by transients, and~essentially yields the fission lifetime. We speculate on the significance of our results for recent experimental observations.

Multiplicities of charged particles prior to fission

“…In this case z is inversely proportional to fl [-10] z ~_l 3-~ ln(IOB:/T). (2) In the overdamped regime [11,12], /~>2co, the fission degree of freedom is strongly damped and as a consequence increases linearly with/~. In both cases, the transients produce an effective fission width which for times t <~ is smaller than the one calculated by Bohr and Wheeler.…”

Nuclear dissipation, fission probability and neutron multiplicity prior to fission

“…With the probability current over the barrier rising smoothly from 0 at time t=0 to the quasistationary value of (1), F~. (t) exhibits a transient behaviour extensively discussed in [2][3][4][5][6][7][8]11]. Let ~(Xo; t) be the probability to find the system to the left of the saddle point Xo, that is inside the collective potential pocket.…”

“…Recently and following the suggestions of [1][2][3] the role of transients in the fission process has been investigated on many different systems [4][5][6][7][8]. These studies focus on the understanding of multiplicities of particles emitted prior to fission in terms of a transport description of this phenomenon.…”

Angular momentum effect in prescission particle multiplicities for a light system by diffusion model

“…Theoretically, many authors derived that the transient time is needed for slow fission mode to attain its stationary decay rate [7][8][9][10][11][12][13][14][15][16][17][18]. In general case, Langevin equation and FokkerPlanck equation is solved analytically with difficulities.…”